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On configuration space integrals for links

Christine Lescop

Geometry & Topology Monographs 4 (2002) 183–199

DOI: 10.2140/gtm.2002.4.183

Abstract

We give an introductory survey on the universal Vassiliev invariant called the perturbative series expansion of the Chern–Simons theory of links in euclidean space, and on its relation with the Kontsevich integral. We also prove an original geometric property of the anomaly of Bott, Taubes, Altschuler, Freidel and D Thurston, that allowed Poirier to prove that the Chern–Simons series and the Kontsevich integral coincide up to degree 6.

Keywords

Kontsevich Integral, Chern–Simons theory, Vassiliev invariants, links, knots, tangles, configuration spaces, quantum invariants, Jacobi diagrams

Mathematical Subject Classification

Primary: 57M27

Secondary: 17B37, 57M25, 81T18

References
Publication

Received: 19 December 2001
Revised: 15 February 2002
Accepted: 22 July 2002
Published: 21 September 2002

Authors
Christine Lescop
CNRS
Institut Fourier
B.P.74
38402 Saint-Martin-d'Hères Cedex
France